[1] 12158 44[1] 44 8Exploratory data analysis & experimental design
January 16, 2024
CHD8 RNA-seq experiment
Gompers et al. (Nature Neuroscience 2017) performed RNA-seq on mice from two different genotypes (18 WT vs 26 CHD8 mutant) and 5 developmental stages
“Using a statistical model that accounted for sex, developmental stage and sequencing batch, we tested for differential expression across 11,936 genes that were robustly expressed”
We’ll use this dataset throughout this lecture to illustrate EDA
Organizing your data: Separated
Option 1 - “Separated”: Keep main data and metadata tables separate
Pros:
Minimal startup effort / extra code
Can be compatible with downstream analysis methods (e.g. Bioconductor)
Cons:
Risky: easy to make a mistake when subsetting and/or reordering samples - extra sanity checks required
Not a convenient format for visualization since main data is separated from its metadata
Overall: not recommended
Organizing your data: Tidy way
Option 2 - “The tidy way”: Combine main data & metadata into one ‘long’ table
Pros:
Unambiguous - keeps all data in one object with one row per observation (e.g. each sample/gene combination is one row, along with all its metadata)
Plays nice with tidyverse tools (e.g. dplyr manipulations, ggplot2 visualization)
Cons:
‘long’ format is inefficient data storage - sample information is repeated
Not compatible with many tools for downstream analysis (e.g. Bioconductor)
Overall: recommended for EDA/visualization
Organizing data: Bioconductor way
Option 3 - “The Bioconductor way”: Combine main data & metadata into one specially formatted object
Pros:
Unambiguous: keeps all data in one object with special slots that can be accessed with handy functions
Plays nice with Bioconductor tools
Efficient storage (no duplication of information like tidy way)
Cons:
Specific to Bioconductor
Not a compatible format for visualization (e.g. ggplot2)
Overall: recommended for downstream analysis (e.g. Differential Expression)
The Bioconductor way: SummarizedExperiment
SummarizedExperiment: A special object format that is designed to contain data & metadataComes along with handy accessor functions
Many related / similar types of objects for specialized data types (e.g.
RangedSummarizedExperiment,SingleCellExperiment,DGEList)
Making sense of the data
Data is what we observe, we want to infer something about “where it came from”
Model of gene expression data generation
The measured expression level of gene \(g\) is the combination of many effects
Analysis goal is often to determine relative role of effects - separate signal from “noise”
Biggest pitfall in (high-dimensional) data analysis
If you don’t look at the data, you are likely going to miss important things
Not just at the beginning, but at every stage
That could mean making plots, or examining numerical patterns - probably both
“Sanity checks” should make up a lot of your early effort
Blindly following recipes/pipelines/vignettes/seminar code → trouble
How to look at the rest of the data?
Sanity check: expression of CHD8
Paper reported that CHD8 went down over time, and is lower in the mutant: confirmed!
Note that we are not doing any formal “analysis” here nor trying to make this plot beautiful – keeping it very simple for our exploration
Two views of the same data: Which do you prefer?
How to best summarize patterns in the data?
Two views of the same data: Let the data speak for itself!
What is the sample size?
Is the distribution symmetrical, or skewed?
Are there any outliers?
Comparing sample distributions: Boxplots
Quick and dirty; reasonable tool to summarize large amounts of data
Not ideal if the distribution is multimodal
Don’t use box plots (alone) when you have small numbers of points; show the points instead!
Comparing distributions: Histograms and Density plots
Don’t use density plots for bounded data
Violin plots
A hybrid of density plots and box plots
Scatter plots
Major problem is ‘over-plotting’ - use transparency or 2D density
Transformations
- Many real data have very skewed distributions – in this case, most values are <500, but there are a smattering up to 10,000
- If your plots look like this, try taking the logarithm
- If have non-positive values (typically 0) add a small constant “pseudocount”
Pairwise (scatter) plots to compare samples
This is nice but unwieldy (or won’t work) for large data sets
Examining the metadata more globally
Sex is not that well balanced
There is a batch confound: The stages were run in different batches (except 17.5 was split in two)
Mapped reads varies with the batches (SeqRun)
Heatmaps
Heatmap of 50 random rows
Revision 1: Same input data; rows are scaled
Rows are scaled to have mean 0 and variance 1 (z-scores)
Subtract the mean; divide by the standard deviation - use
scale()on the data rows (some packages will do this by default)It is now easier to compare the rows and see a bit of structure
Revision 2: adjusting contrast
Range of values is clipped to (-2,2): aything more than two SDs from the row mean is set to 2
Limit values of 2 or 3 SDs are common
Clipping hides outliers but allows us to see variation in the bulk of the data
Plotting too much data
An entire data set (>10k rows)
If the cells are less than 1 pixel, everything starts to turn to mush and can even be misleading
If your heatmap has too many rows to see labels (genes), make sure it is conveying useful information (what are you trying to show?)
Choice of colours
- Humans can’t really tell the difference between a 8- and 16-colour scale
- Many R defaults, other common scales (green/red) not colourblind friendly
RColorBrewer: scales based on work of visualization experts- Greyscale: loss of dynamic range, but cheaper to publish!
Divergent vs. sequential maps
Divergent: colours pass through black or white at the midpoint (e.g. mean). Ideal if your original data are naturally “symmetric” around zero (or some other value) - Otherwise it might just be confusing
Sequential: colours go from light to dark. Darker colours mean “higher” by default in RColorBrewer. No defined midpoint.
A confusing heat map (Matlab)
Too many different colours to readily interpret relative ordering of values
Not recommended to use these types of scales for continuous values
Rainbows or scales with many distinct colours are better for factors / categorical variables
Heatmap recommendations
Pick an appropriate colour scale
Show a scale bar (so don’t use
base::heatmap)Either cluster rows / columns, or order by something meaningful (e.g. sample info)
Add annotation bars of meaningful covariates
If you have missing data points, make sure it is obvious where they are (e.g. different colour)
Experimental design and quality
Fig 1, 10.1038/sj.ebd.6400436
Batch effects
“Batch effects are sub-groups of measurements that have qualitatively different behaviour across conditions and are unrelated to the biological or scientific variables in a study”
Leek et al. 2010 Nature Rev. Genetics 11:733
Magnitude of batch effects vary
Consider correcting for them if possible - batch artifact detection and correction will be covered in more detail in a later lecture
A basic but effective outlier detection method
A heatmap of the sample-sample correlation matrix (generally a useful diagnostic plot)
Expect correlations to be tighter within experimental groups than across groups
There are no firm guidelines for evaluating this … but you could apply a rule like “out of >1.5 IQR”
In practice, outliers are often pretty obvious
